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Chapter 11:Capital Budgeting and Risk Analysis

2002, Prentice Hall, Inc.

Project Standing

Alone Risk

Risk

diversified away

within firm as this

project is combined

with firm’s other

projects and assets

Three Measures of a Project’s RiskProject Standing

Alone Risk

Risk

diversified away

within firm as this

project is combined

with firm’s other

projects and assets

Project’s

contribution-

to-firm risk

Three Measures of a Project’s RiskProject Standing

Alone Risk

Risk

diversified away

within firm as this

project is combined

with firm’s other

projects and assets

Project’s

contribution-

to-firm risk

Risk

diversified away

by shareholders as

securities are combined

to form diversified

portfolio

Three Measures of a Project’s RiskProject Standing

Alone Risk

Risk

diversified away

within firm as this

project is combined

with firm’s other

projects and assets

Project’s

contribution-

to-firm risk

Risk

diversified away

by shareholders as

securities are combined

to form diversified

portfolio

Systematic risk

Three Measures of a Project’s RiskIncorporating Risk into Capital Budgeting

Two Methods:

- Certainty Equivalent Approach
- Risk-Adjusted Discount Rate

n

t=1

S

ACFt

(1 + k)

NPV = - IO

t

How can we adjust this model to take risk into account?- Adjust the After-tax Cash Flows (ACFs), or
- Adjust the discount rate (k).

Certainty Equivalent Approach

- Adjusts the risky after-tax cash flows to certain cash flows.
- The idea:

Certainty Equivalent Approach

- Adjusts the risky after-tax cash flows to certain cash flows.
- The idea:

Risky Certainty Certain

Cash XEquivalent = Cash

Flow Factor (a) Flow

Certainty Equivalent Approach

Risky Certainty Certain

Cash X Equivalent = Cash

Flow Factor (a) Flow

Risky “safe”

$1000 .70 $700

Certainty Equivalent Approach

Risky Certainty Certain

Cash X Equivalent = Cash

Flow Factor (a) Flow

Risky “safe”

$1000 .95 $950

The greater the risk associated with a particular cash flow, the smaller the CE factor.

Certainty Equivalent Approach

- Steps:

1) Adjust all after-tax cash flows by certainty equivalent factors to get certain cash flows.

2) Discount the certain cash flows by the risk-free rate of interest.

Incorporating Risk into Capital Budgeting

- Risk-Adjusted Discount Rate

n

t=1

S

ACFt

(1 + k)

NPV = - IO

t

How can we adjust this model to take risk into account?- Adjust the discount rate (k).

Risk-Adjusted Discount Rate

- Simply adjust the discount rate (k) to reflect higher risk.
- Riskier projects will use higher risk-adjusted discount rates.
- Calculate NPV using the new risk-adjusted discount rate.

Risk-Adjusted Discount Rates

- How do we determine the appropriate risk-adjusted discount rate (k*) to use?
- Many firms set up risk classes to categorize different types of projects.

Risk Classes

Risk RADR

Class (k*) Project Type

1 12% Replace equipment,

Expand current business

2 14% Related new products

3 16% Unrelated new products

4 24% Research & Development

Summary: Risk and Capital Budgeting

You can adjust your capital budgeting methods for projects having different levels of risk by:

- Adjusting the discount rate used (risk-adjusted discount rate method),
- Measuring the project’s systematic risk,
- Computer simulation methods,
- Scenario analysis,
- Sensitivity analysis.

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